### How does gravity interact with a photon?

• If photon is mass-less and gravity can interact only with matter, then how does gravity alter the trajectory of light?

Maybe it's the curvature of the space time that affects the light?

@Archa It does. The path of light is defined in terms of geodesics ("shortest small paths", loosely) in the space-time manifold, which are determined (in a certain sense) by the curvature. But as Stan points out, a lot more than mass, or even mass+energy, contributes to gravity in GR.

It is perhaps worth noting that Newton could have modelled quite accurately the deflection of light using his corpuscular theory of light and the principle that gravitational acceleration is independent of mass (or the lack of it) http://arxiv.org/abs/physics/0508030

7 years ago

It is simply not true that gravity can only interact with mass. Rather, any long-range spin-2 force interacts with all energy-momentum equally, and it source is the stress-energy-momentum tensor. That is one way to state the equivalence principle.

Note that a massive object in its own rest frame has an associated energy \$E = mc^2\$, which under ordinary conditions is usually much higher than any stress terms (including pressure) or momentum (outside the rest frame). Thus one can usually pretend that gravity couples to mass, but it isn't so--rather, the gravitational charge is energy, and the entire stress-energy-momentum tensor couples to the gravitational field. This is analogous to how for electromagnetism, there is electric charge, but the electric currents also make a difference.

In the weak-field limit of general relativity, one can consider the fact that light is gravitationally deflected twice as much as a naive Newtonian prediction would be (for an object at the speed of light under Newtonian mechanics, that is) as the fault of light putting a pressure in the direction of its propagation equal to its energy density. But in general, the motion of a test particle is determined by its four-velocity and the geometry of spacetime only, and the light would just be a special case of having a 'lightlike' four-velocity.